The 33-year-old striker has dropped down the pecking order at the club behind Tammy Abraham and has managed only two starts in the Premier League this season.
Chelsea are preparing to sign a new striker, and Frank Lampard is prepared to let the French international depart midway through the season.
This is a perfect opportunity for Everton to snap him up on a cut-price deal.
Everton have managed to score 19 goals in the Premier League so far, and the Toffees are heavily reliant on Richarlison, who is not an out an out striker.
Dominic Calvert-Lewin can turn out to be a superstar in the future but as of now, there is little evidence that he can score 15-20 goals in a season.
Cenk Tosun has turned out to be a big flop and his future remains unclear. Giroud can be a short-term solution for the club.
He will add quality and depth to the side, and would be a smart piece of business for the Toffees if they can agree a deal for him.